Multilevel Picard approximations for McKean-Vlasov stochastic differential equations

Martin Hutzenthaler; Thomas Kruse; Tuan Anh Nguyen

doi:10.1016/j.jmaa.2021.125761

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arXiv · 2103.10870

Multilevel Picard approximations for McKean-Vlasov stochastic differential equations

Martin Hutzenthaler·Thomas Kruse·Tuan Anh Nguyen

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Abstract

In the literatur there exist approximation methods for McKean-Vlasov stochastic differential equations which have a computational effort of order $3$. In this article we introduce full-history recursive multilevel Picard (MLP) approximations for McKean-Vlasov stochastic differential equations. We prove that these MLP approximations have computational effort of order $2+$ which is essentially optimal in high dimensions.

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Martin Hutzenthaler, Thomas Kruse, Tuan Anh Nguyen. 2021-03-19. Multilevel Picard approximations for McKean-Vlasov stochastic differential equations. https://doi.org/10.1016/j.jmaa.2021.125761

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